Cancer treatment development is a complex process, with tumor heterogeneity and inter-patient variations limiting the success of therapeutic intervention. Traditional two-dimensional cell culture has been used to study cancer metabolism, but it fails to capture physiologically relevant cell-cell and cell-environment interactions required to mimic tumor-specific architecture. Over the past three decades, research efforts in the field of 3D cancer model fabrication using tissue engineering have addressed this unmet need. The self-organized and scaffold-based model has shown potential to study the cancer microenvironment and eventually bridge the gap between 2D cell culture and animal models. Recently, three-dimensional (3D) bioprinting has emerged as an exciting and novel biofabrication strategy aimed at developing a 3D compartmentalized hierarchical organization with the precise positioning of biomolecules, including living cells. In this review, we discuss the advancements in 3D culture techniques for the fabrication of cancer models, as well as their benefits and limitations. We also highlight future directions associated with technological advances, detailed applicative research, patient compliance, and regulatory challenges to achieve a successful bed-to-bench transition.